Born in Hanau, near Frankfurt am Main, Hindemith was taught the violin as a child. He entered Frankfurt's Hoch’sche Konservatorium, where he studied violin with Adolf Rebner, as well as conducting and composition with Arnold Mendelssohn and Bernhard Sekles. At first he supported himself by playing in dance bands and musical-comedy groups. He became deputy leader of the Frankfurt Opera Orchestra in 1914, and was promoted to leader in 1917. He played second violin in the Rebner String Quartet from 1914. In 1921 he founded the Amar Quartet, playing viola, and extensively toured Europe.
In 1922, some of his pieces were played in the International Society for Contemporary Music festival at Salzburg, which first brought him to the attention of an international audience. The following year, he began to work as an organizer of the Donaueschingen Festival, where he programmed works by several avant garde composers, including Anton Webern and Arnold Schoenberg. From 1927 he taught composition at the Berliner Hochschule für Musik in Berlin. Hindemith wrote the music for Hans Richter's 1928 avant-garde film Ghosts Before Breakfast (Vormittagsspuk), although the score was subsequently lost, and he also acted in the film. In 1929 he played the solo part in the premiere of William Walton's Viola Concerto, after Lionel Tertis, for whom it was written, turned it down.
During the 1930s he made a visit to Cairo and several visits to Ankara where (at the invitation of Mustafa Kemal Atatürk) he led the task of reorganizing Turkish music education and the early efforts for the establishment of Turkish State Opera and Ballet. Towards the end of the 1930s, he made several tours in America as a viola and viola d'amore soloist.
Hindemith's relationship to the Nazis is a complicated one. Some condemned his music as "degenerate" (largely on the basis of his early, sexually charged operas such as Sancta Susanna), and in December 1934, during a speech at the Berlin Sports Palace, Germany’s Minister of Propaganda, Joseph Goebbels publicly denounced Hindemith as an "atonal noisemaker."
Other officials working in Nazi Germany, though, thought that he might provide Germany with an example of a modern German composer, who by this time was writing music based in tonality, and with frequent references to folk music; the conductor Wilhelm Furtwängler's defense of Hindemith, published in 1934, takes precisely this line.
The controversy around his work continued throughout the thirties, with the composer falling in and out of favor with the Nazi hierarchy; he finally emigrated to Switzerland in 1938 (in part because his wife was of partially Jewish ancestry).
In 1935, Hindemith was commissioned by the Turkish government to reorganize that country's musical education, and, more specifically, was given the task of preparing material for the "Universal and Turkish Polyphonic Music Education Programme" for all music-related institutions in Turkey, a feat which he accomplished to universal acclaim.
This development seems to have been supported by the Nazi regime: it may have got him conveniently out of the way, yet at the same time he propagated a German view of musical history and education. (Hindemith himself said he believed he was being an ambassador for German culture.)
Hindemith did not stay in Turkey as long as many other émigrés. Nevertheless, he greatly influenced the developments of Turkish musical life; the Ankara State Conservatory owes much to his efforts. In fact, Hindemith was regarded to be a "real master" by young Turkish musicians and he was appreciated and greatly respected.
In 1940, Hindemith emigrated to the United States. At the same time that he was codifying his musical language, his teaching and compositions began to be affected by his theories, according to critics like Ernest Ansermet. Once in the U.S. he taught primarily at Yale University where he had such notable students as Lukas Foss, Graham George, Norman Dello Joio, Mel Powell, Harold Shapero, Hans Otte, Ruth Schonthal, and Oscar-winning film director George Roy Hill. During this time he also gave the Charles Eliot Norton Lectures at Harvard, from which the book A Composer's World was extracted (Hindemith 1952). Hindemith had a long friendship with Erich Katz, whose own compositions were influenced by him.
He became an American citizen in 1946, but returned to Europe in 1953, living in Zürich and teaching at the university there. Towards the end of his life he began to conduct more, and made numerous recordings, mostly of his own music.
An anonymous critic writing in Opera magazine in 1954, having attended a performance of Hindemith's Neues vom Tage, noted that "Mr Hindemith is no virtuoso conductor, but he does possess an extraordinary knack of making performers understand how his own music is supposed to go". He was awarded the Balzan Prize in 1962.
After a prolonged decline in his physical health (though he kept composing until almost the last), Hindemith died in Frankfurt from pancreatitis at the age of 68.